### Speaker

### Description

The usual Swiss-Cheese operad encodes triplets (A,B,f), where A is an algebra over the little disks operad in dimension n (i.e., an \mathsf{E}*n-algebra), B is an \mathsf{E}*{n-1}-algebra, and f : A \to Z(B) is a central morphism of E_n-algebras.

The Swiss-Cheese operad admits several variants and generalizations. In Voronov's original version, the morphism is replaced by an action A \otimes B \to B; in the extended Swiss-Cheese operad ESC_{mn}, the lower algebra is an \mathsf{E}*m-algebra for some m < n; and in the complementarily-constrained disks operad \mathsf{CD}*{mn}, the morphism is replaced by a derivation f + \epsilon \delta : A \to B[\epsilon].

In this talk, I will explain approaches to prove the (non-)formality of some of the variants of the Swiss-Cheese operad, including a joint work in progress with Renato Vasconcellos Vieira.